Problem: Emelia registers vehicles for the Department of Transportation. Sports utility vehicles (SUVs) make up $12\%$ of the vehicles she registers. Let $V$ be the number of vehicles Emelia registers in a day until she first registers an SUV. Assume the type of each vehicle is independent. Find the probability that Emelia registers more than $4$ vehicles before she registers an SUV. You may round your answer to the nearest hundredth. $P(V>4)=$
Explanation: Without a fancy calculator For each vehicle: $P({\text{SUV}})=0.12$ $P(\text{not}})=0.88$ If Emelia registers more than $4$ vehicles before she registers an SUV, then the first $4$ vehicles must not be SUVs. $\begin{aligned} P(V>4)&=P(\text{4 not SUVs}) \\\\ &=(0.88})^4 \\\\ &\approx 0.5997 \end{aligned}$ $P(V>4)\approx 0.5997 \approx 0.6$